On the inverse scattering transform of a nonlinear evolution equation with 2+1 dimensions related to nonstrict hyperbolic systems

Abstract

We introduce a nonlinear 2 + 1 dimensional system of equations related to the first-order nonstrict hyperbolic system. On the basis of the analysis of Gelfand-Levitan-Marchenko (GLM) type integral equations corresponding to the inverse scattering problem for the first-order nonstrict hyperbolic system on the whole plane, we obtain a class of exact solutions of some nonlinear equations with 2 + 1 dimensions.